This PhD thesis examines the thermodynamical properties of spin-1/2 Heisenberg chains which are coupled to Einstein phonons. One result of this study is that these spin-phonon systems undergo a phase transition similar to a spin-Peierls transition (cf. Physical Review B 60 (1999) 12125-12133 and Physical Review B 65 (2002) 144438). Another result is that in the undimerized phase the critical exponent nu depends on both the phonon frequency and the spin-phonon coupling constant. This means that these spin-phonon systems change the universality class continuously with the spin-phonon coupling (cf. arXiv: cond-mat/9912150v1).This PhD thesis examines the thermodynamical properties of spin-1/2 Heisenberg chains which are coupled to Einstein phonons. One result of this study is that these spin-phonon systems undergo a phase transition similar to a spin-Peierls transition (cf. Physical Review B 60 (1999) 12125-12133 and Physical Review B 65 (2002) 144438). Another result is that in the undimerized phase the critical exponent nu depends on both the phonon frequency and the spin-phonon coupling constant. This means that these spin-phonon systems change the universality class continuously with the spin-phonon coupling (cf. arXiv: cond-mat/9912150v1).

Mar 11, 20190 citations

Thermodynamic properties of the Heisenberg chain with spin S = 1

Qing Jiang, Hai‐Xia Cao, Zhen‐Ya Li

Physics Letters AOct 1, 19963 citations

Critical Behavior of the Isotropic Ferromagnetic Quantum Heisenberg Chain

P. Schlottmann

The thermodynamic Bethe-Ansatz equations for the isotropic ferromagnetic $S=\frac{1}{2}$ Heisenberg chain have been solved numerically. At low temperatures, I find a power-law dependence on $T$ for the specific heat and the susceptibility with critical exponents $\ensuremath{\alpha}=\ensuremath{-}0.49\ifmmode\pm\else\textpm\fi{}0.02$, $\ensuremath{\gamma}=2.00\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\Delta}\ensuremath{\simeq}\ensuremath{\gamma}$. The exponent $\ensuremath{\alpha}$ is compatible with effective spin waves and $\ensuremath{\gamma}$ and $\ensuremath{\Delta}$ are the exponents of the classical chain. Amplitudes and corrections to scaling are obtained and differences with previous results are discussed.The thermodynamic Bethe-Ansatz equations for the isotropic ferromagnetic $S=\frac{1}{2}$ Heisenberg chain have been solved numerically. At low temperatures, I find a power-law dependence on $T$ for the specific heat and the susceptibility with critical exponents $\ensuremath{\alpha}=\ensuremath{-}0.49\ifmmode\pm\else\textpm\fi{}0.02$, $\ensuremath{\gamma}=2.00\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\Delta}\ensuremath{\simeq}\ensuremath{\gamma}$. The exponent $\ensuremath{\alpha}$ is compatible with effective spin waves and $\ensuremath{\gamma}$ and $\ensuremath{\Delta}$ are the exponents of the classical chain. Amplitudes and corrections to scaling are obtained and differences with previous results are discussed.

Physical Review LettersMay 13, 198570 citations

The thermodynamic Bethe-Ansatz equations for the isotropic ferromagnetic

S=\frac{1}{2}

Heisenberg chain have been solved numerically. At low temperatures, I find a power-law dependence on

T

for the specific heat and the susceptibility with critical exponents $\ensuremath{\alpha}=\ensuremath{-}0.49\ifmmode\pm\else\textpm\fi{}0.02$, $\ensuremath{\gamma}=2.00\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\Delta}\ensuremath{\simeq}\ensuremath{\gamma}$. The exponent $\ensuremath{\alpha}$ is compatible with effective spin waves and $\ensuremath{\gamma}$ and $\ensuremath{\Delta}$ are the exponents of the classical chain. Amplitudes and corrections to scaling are obtained and differences with previous results are discussed.